it's supposed to heal 2 pts whenever it kills an opponent. you should see a green +2 pop up over him, followed by a purple +3 for the 3 culture that he gets. however, if you get damaged 5 then healed +2 you'll still be down 3 total. I'm playing an aztec game right now and it's definitely working correctly for me.
btw, that is a great early UU advantage imho. for aztecs the jaguar->sword->longsword path can be quite effective.